Here we assume the system to be antiferromagnetic, i.e., \(\Delta >0\) . On the half-plane with \(\Delta >0\) , there are three distinct phases: a Haldane phase, a large-D phase, and a Néel phase [1]}. All these phases have a finite energy gap above the ground state [2]}. The phase diagram of spin-1 Heisenberg XXZ with a uniaxial single-ion anisotropy is shown in Fig.REF  by use of the quantum renormalization group (QRG) method described below. For a large negative single-ion anisotropy, i.e., \(D\ll -2\) , the system prefers the \(|\uparrow \rangle \)  and \(|\downarrow \rangle \)  states rather than the \(|0\rangle \)  state. Hence, one expects that the Néel order parameter is non-zero, which corresponds to the Néel phase [3]}. On the other hand, for a large positive single-ion anisotropy, i.e., \(D\gg 2\) , the system prefers the \(|0\rangle \)  state in the large-D phase, and thus all the spin-spin correlations are expected to be short ranged [3]}.
